The panino con abbacchio takes a Roman roast off the Sunday table and folds it into bread. Abbacchio is milk-fed lamb, slaughtered very young so the meat is pale, tender, and mild rather than the strong, gamey register of older lamb. Roasted Roman-style, al forno or alla scottadito, with rosemary, garlic, and a little anchovy worked into the fat, it comes out soft enough to shred and gentle enough that the bread does not have to fight it. The defining fact is that the filling is a finished roast, not a cured or grilled thing assembled at a counter, and the sandwich is a way to make a plated dish portable rather than a construction in its own right.
The craft is keeping a roast behaving between two slices. The lamb is pulled or sliced off the bone and the herbed pan fat is what seasons it through, so every bite carries rosemary and the anchovy's quiet salt rather than tasting only of meat. A roll is chosen sturdy and is often warmed or lightly toasted so it survives the fat without going slack, and the portion is kept controlled because an overfilled one collapses the moment it is bitten. There is no sauce added: a properly roasted abbacchio arrives already complete, and the restraint is in not stacking anything onto a dish that was finished in the oven. It is eaten warm or at room temperature, when the fat reads softest and the meat has not tightened.
The variations stay Roman and stay on the same roast: the scottadito chop stripped into bread against the slow al forno shoulder, the version that adds the bitter cicoria ripassata the dish is plated with, the one carrying the pan juices spooned in. Each of those is a different Roman lamb preparation given a handle, and each deserves its own article rather than being crowded in here.